David Makinson – författare

This easy-to-understand textbook introduces the mathematical language and problem-solving tools essential to anyone wishing to enter the world of computer and information sciences. Specifically designed for the student who is intimidated by mathematics, the book offers a concise treatment in an engaging style.The thoroughly revised third edition features a new chapter on relevance-sensitivity in logical reasoning and many additional explanations on points that students find puzzling, including the rationale for various shorthand ways of speaking and ‘abuses of language’ that are convenient but can give rise to misunderstandings. Solutions are now also provided for all exercises.Topics and features: presents an intuitive approach, emphasizing how finite mathematics supplies a valuable language for thinking about computation; discusses sets and the mathematical objects built with them, such as relations and functions, as well as recursion and induction; introduces core topics of mathematics, including combinatorics and finite probability, along with the structures known as trees; examines propositional and quantificational logic, how to build complex proofs from simple ones, and how to ensure relevance in logic; addresses questions that students find puzzling but may have difficulty articulating, through entertaining conversations between Alice and the Mad Hatter; provides an extensive set of solved exercises throughout the text.This clearly-written textbook offers invaluable guidance to students beginning an undergraduate degree in computer science. The coverage is also suitable for courses on formal methods offered to those studying mathematics, philosophy, linguistics, economics, and political science. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study.

area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.

area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.

This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.

The first part of this preface is for the student; the second for the instructor. But whoever you are, welcome to both parts. For the Student You have finished secondary school, and are about to begin at a university or technical college. You want to study computing. The course includes some mathematics { and that was not necessarily your favourite subject. But there is no escape: some finite mathematics is a required part of the first year curriculum. That is where this book comes in. Its purpose is to provide the basics { the essentials that you need to know to understand the mathematical language that is used in computer and information science. It does not contain all the mathematics that you will need to look at through the several years of your undergraduate career. There are other very good, massive volumes that do that. At some stage you will probably find it useful to get one and keep it on your shelf for reference. But experience has convinced this author that no matter how good the compendia are, beginning students tend to feel intimidated, lost, and unclear about what parts to focus on. This short book, on the other hand, offers just the basics which you need to know from the beginning, and on which you can build further when needed.

This easy-to-understand textbook introduces the mathematical language and problem-solving tools essential to anyone wishing to enter the world of computer and information sciences. Specifically designed for the student who is intimidated by mathematics, the book offers a concise treatment in an engaging style.

The thoroughly revised third edition features a new chapter on relevance-sensitivity in logical reasoning and many additional explanations on points that students find puzzling, including the rationale for various shorthand ways of speaking and ‘abuses of language’ that are convenient but can give rise to misunderstandings. Solutions are now also provided for all exercises.

Topics and features: presents an intuitive approach, emphasizing how finite mathematics supplies a valuable language for thinking about computation; discusses sets and the mathematical objects built with them, such as relations and functions, as well as recursion and induction; introduces core topics of mathematics, including combinatorics and finite probability, along with the structures known as trees; examines propositional and quantificational logic, how to build complex proofs from simple ones, and how to ensure relevance in logic; addresses questions that students find puzzling but may have difficulty articulating, through entertaining conversations between Alice and the Mad Hatter; provides an extensive set of solved exercises throughout the text.

This clearly-written textbook offers invaluable guidance to students beginning an undergraduate degree in computer science. The coverage is also suitable for courses on formal methods offered to those studying mathematics, philosophy, linguistics, economics, and political science. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study.